论文标题
阿贝尔亚群的定义领域
Fields of definition of abelian subvarieties
论文作者
论文摘要
在本文中，我们研究了Abelian Subvarieties的定义字段$ b \ subset a _ {\ overline {k}} $对于Abelian品种的特征性$ 0 $的字段$ k $。我们表明，规定没有$ a _ {\叠加{k}} $的同种型组件很简单，有无限的许多Abelian subvarieties $ a _ {\ overline {k overline {k}} $，带有定义$ k_a $的字段$ k_a $的定义领域，$ a _;该结果与雷蒙德（Rémond）的早期作品相结合，为最小程度的最小度提供了明显的最大程度，在该范围扩展中，ABELIAN子不同$ a _ {\ overline {k}} $的定义是用不同的固定尺寸和特征性$ 0 $ 0 $的$ a $ a $ a $ a $ k $定义的。
In this paper we study the field of definition of abelian subvarieties $B\subset A_{\overline{K}}$ for an abelian variety $A$ over a field $K$ of characteristic $0$. We show that, provided that no isotypic component of $A_{\overline{K}}$ is simple, there are infinitely many abelian subvarieties of $A_{\overline{K}}$ with field of definition $K_A$, the field of definition of the endomorphisms of $A_{\overline{K}}$. This result combined with earlier work of Rémond gives an explicit maximum for the minimal degree of a field extension over which an abelian subvariety of $A_{\overline{K}}$ is defined with varying $A$ of fixed dimension and $K$ of characteristic $0$.
